for
, where is the
unit direction vector at angle .
The angular distribution can be uniform
in the range , giving
.
A slight improvement results if there is more concentration in the
directions perpendicular to the billiard's
largest distances from the origin.
In the 2-by-4 stadium (following [195]) I used
.

Note that Li[137] claims
he can half the RPW basis set size required, by randomizing phases
(removing the need for both cos and sin functions).
From our considerations in Section 5.3.1, it seems unlikely that
he has somehow defeated the semiclassical basis size requirement by a factor
of 2, however this is an area for investigation.